One refined passport of genus 8 with automorphism group $C_2.S_4$

• Label: 8.48-28.0.3-4-8.2
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(C_2.S_4\)
• Signature: \([ 0; 3, 4, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$C_2.S_4$
Group identifier:	$[48,28]$
Signature:	$[ 0; 3, 4, 8 ]$

Conjugacy classes for this refined passport:

$3, 5, 8$

Jacobian variety group algebra decomposition:	$A_{4}\times A_{2}^{2}$
Corresponding character(s):	$4, 8$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^4-1)(x^{12}-33x^8-33x^4+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.48-28.0.3-4-8.2.1

	(1,9,17) (2,10,18) (3,15,22) (4,16,21) (5,12,24) (6,11,23) (7,14,19) (8,13,20) (25,33,41) (26,34,42) (27,39,46) (28,40,45) (29,36,48) (30,35,47) (31,38,43) (32,37,44)
	(1,32,2,31) (3,27,4,28) (5,30,6,29) (7,26,8,25) (9,48,10,47) (11,43,12,44) (13,46,14,45) (15,42,16,41) (17,40,18,39) (19,35,20,36) (21,38,22,37) (23,34,24,33)
	(1,43,6,47,2,44,5,48) (3,45,7,41,4,46,8,42) (9,35,14,39,10,36,13,40) (11,37,15,33,12,38,16,34) (17,27,22,31,18,28,21,32) (19,29,23,25,20,30,24,26)